{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "# Berechnung Umfang eines Kreises\n",
    "def umfang(r : float) -> float:\n",
    "    return 2 * r * math.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Berechnung der wurzel durch ausprobieren\n",
    "\n",
    "def wurzel(z):\n",
    "    for n in range(100):\n",
    "        if n ** 2 == z:\n",
    "            return n\n",
    "    return -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Multi-Return\n",
    "\n",
    "def multi_return():\n",
    "    return (42, 23)\n",
    "\n",
    "a,b = multi_return(42,23)\n",
    "\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "101\n"
     ]
    }
   ],
   "source": [
    "# variable Anzahl an Argumenten\n",
    "\n",
    "# mögliche Implementierung eine max-Funktion\n",
    "def max(*a):\n",
    "    result = a[0]\n",
    "    for i in a:\n",
    "        if result < i:\n",
    "            result = i\n",
    "    return result\n",
    "\n",
    "print(max(4,5,34,78,12,101))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20\n",
      "20\n",
      "20\n"
     ]
    }
   ],
   "source": [
    "# named arguments\n",
    "\n",
    "def calc(zahl1, zahl2):\n",
    "    return 2 * zahl1 + 4 * zahl2\n",
    "\n",
    "print(calc(2,4))\n",
    "\n",
    "print(calc(zahl1=2, zahl2=4))\n",
    "print(calc(zahl2=4, zahl1=2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 4 16 256\n"
     ]
    }
   ],
   "source": [
    "# default arguments\n",
    "\n",
    "def potenz(basis = 2, exponent = 1):\n",
    "    return basis ** exponent\n",
    "\n",
    "a = potenz()\n",
    "b = potenz(4)\n",
    "c = potenz(2,4)\n",
    "\n",
    "d = potenz(exponent=8)\n",
    "\n",
    "print(a,b,c,d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16\n"
     ]
    }
   ],
   "source": [
    "# Funktionen sind Objekte\n",
    "\n",
    "def twice(f,x):\n",
    "    return f(f(x))\n",
    "\n",
    "def quadriere(x):\n",
    "    return x*x\n",
    "\n",
    "print(twice(quadriere, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "# global\n",
    "\n",
    "x = 0\n",
    "\n",
    "def incr_x2():\n",
    "    global x\n",
    "    x = x + 1\n",
    "\n",
    "incr_x2()\n",
    "\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "12\n"
     ]
    }
   ],
   "source": [
    "# verschachtelte Funktionen\n",
    "\n",
    "def function1(x):\n",
    "    def function2(y):\n",
    "        print(y + 2)\n",
    "        return y + 2\n",
    "    return 3 * function2(x)\n",
    "\n",
    "a = function1(2)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "# Lambdas\n",
    "\n",
    "# klassische Funktionsdefinition\n",
    "def add(a,b):\n",
    "    return a + b\n",
    "\n",
    "# Definition über Lambda\n",
    "add2 = lambda a,b : a + b\n",
    "\n",
    "print(add(1,2))\n",
    "print(add2(2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 4, 6, 8]\n"
     ]
    }
   ],
   "source": [
    "# Listen und Lambda\n",
    "\n",
    "my_list = list(range(1,9))\n",
    "gerade = list(filter(lambda e: e% 2 == 0, my_list))\n",
    "\n",
    "print(gerade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['PULP FICTION', 'KILL BILL', 'RESERVOIR DOGS']\n"
     ]
    }
   ],
   "source": [
    "# Listen und Lambda\n",
    "\n",
    "filme = [\"Pulp Fiction\", \"Kill Bill\", \"Reservoir Dogs\"]\n",
    "filme_gross = list(map(lambda f: f.upper(), filme))\n",
    "\n",
    "print(filme_gross)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "import functools\n",
    "\n",
    "a = [1,2,3,4]\n",
    "\n",
    "r = functools.reduce(lambda sum, x: sum + x, a)\n",
    "\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fak(n):\n",
    "    return n * fak(n - 1) if n > 1 else 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24\n"
     ]
    }
   ],
   "source": [
    "def fak(n):\n",
    "    ergebnis = 1\n",
    "\n",
    "    for i in range(2, n+1):\n",
    "        ergebnis *= i\n",
    "    \n",
    "    return ergebnis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fibonacci-Folge\n",
    "\n",
    "def fibonacci(n : int) -> int:\n",
    "    if n == 1 or n == 2:\n",
    "        return n\n",
    "    return fibonacci(n-1) + fibonacci(n-2)"
   ]
  }
 ],
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